Evaluation of Phase-Diversity Techniques for Solar-Image Restoration

Abstract

Phase-diversitytechniques provide a novel observational method for overcomming the effects of turbulence and instrument-induced aberrations in ground-based astronomy. Two implementations of phase-diversity techniques that differ with regard to noise model, estimator, optimization algorithm, method of regularization, and treatment of edge effects are described. Reconstructions of solar granulation derived by applying these two implementations to common data sets are shown to yield nearly identical images. For both implementations, reconstructions from phase-diverse speckle data (involving multiple realizations of turbulence) are shown to be superior to those derived from conventional phase-diversity data (involving a single realization). Phase-diverse speckle reconstructions are shown to achieve near diffraction-limited resolution and are validated by internal and external consistency tests, including a comparison with a reconstruction using a well-accepted speckle-imaging method.

Phase diversity restoration of sunspot images

“…The arrow in the centre of the sunspot points to the solar disc centre. Paxman et al 1992;Löfdahl & Scharmer 1994;Paxman et al 1996). This technique allows a subtantial correction for the aberrations induced by both the telescope and the turbulent terrestrial atmosphere.…”

Phase diversity restoration of sunspot images

“…A few papers in the literature are complementary in the description of the PD technique for image reconstruction (e.g. Gonsalves & Childlaw 1979;Gonsalves 1982;Paxman et al 1992;Löfdahl & Scharmer 1994;Paxman et al 1996). However, we summarize the most relevant items of the method as an introduction to this powerful tool for high resolution solar imaging and to report on our particular setting of parameters and assumptions to run the computing code.…”

“…To circumvent this problem, we combine in a sort of speckle summation (see e.g. Paxman et al 1996) the results of the inversion of 3 or 4 image pairs taken close in time, so that evolutionary aspects in the solar structures can be neglected. The lower right panel of Fig.…”

Two dual-wavelength sequences of high-resolution solar photospheric images captured over several hours and restored by use of phase diversity

“…This is accomplished by use of simultaneous images taken in different focus positions, where information about the object and the instantaneous wavefront at the time of exposure are encoded in linearly independent ways. We refer to techniques, where several pairs of PD data with a common object are used to make a single restored frame, as phase-diverse speckle (PDS) methods (Paxman et al 1996). A small number of atmospheric realizations is sufficient for good restorations, significantly reducing the amount of data needed compared to speckle imaging methods.…”

“…A PD data set with the required characteristics was collected and restored from seeing effects by Löfdahl (1996), Löfdahl et al (1998, henceforth Paper I). The bright point dynamics in the resulting 70-min data sequence was analyzed by Berger et al (1998a,b), van Ballegooijen et al (1998), van Ballegooijen & Nisenson (1999, Krishnakumar & Venkatakrishnan (1999), Hasan et al (2000), Lawrence et al (2001).…”